A note on the use of analytic signal in the pseudo Wigner distribution

The pseudo-Wigner distribution (PWD) is a modified version of the Wigner distribution (WD) which is currently used to obtain a time-frequency representation of a signal by applying the WD to successive slices of the signal. The application of the WD to the analytic signal associated with the real signal presents many advantages. The exact consequences of using the analytic signal in the PWD have scarcely been examined. Indeed, if the PWD is applied directly to the analytic signal, the selected slices are not necessarily analytic. Otherwise the PWD can be applied to the analytic signal associated with each slice. A study is made of the consequences of these different definitions on the result and of which procedure is best to apply